CASINO manual - Theory of Condensed Matter

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19.3 The core-polarization potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 19.4 Evaluation of infinite Coulomb sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 20 Model interactions 145 20.1 Square-well interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 20.2 Modified Pöschl-Teller interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 20.3 Hard sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 21 Multi-determinant expansions 145 21.1 Compressed multi-determinant expansions . . . . . . . . . . . . . . . . . . . . . . . . . 146 22 The Jastrow factor 146 22.1 General form of CASINO’s Jastrow factor . . . . . . . . . . . . . . . . . . . . . . . . . 146 22.2 The u, χ and f terms in the Jastrow factor . . . . . . . . . . . . . . . . . . . . . . . . 147 22.3 The RPA form of the u term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 22.4 The p and q terms in the Jastrow factor . . . . . . . . . . . . . . . . . . . . . . . . . . 148 22.5 The three-body W term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 23 Backflow transformations 149 23.1 The generalized backflow transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 149 23.2 Constraints on the backflow parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 150 23.3 Improving the nodes of Ψ T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 24 Statistical analysis of data 152 24.1 The reblocking method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 24.2 Estimate of the correlation time given by CASINO . . . . . . . . . . . . . . . . . . . . 153 24.3 Estimating equilibration times and correlation periods . . . . . . . . . . . . . . . . . . 154 25 Wave-function optimization 154 25.1 Variance minimization: the standard method . . . . . . . . . . . . . . . . . . . . . . . 154 25.2 Variance minimization: the ‘varmin-linjas’ method . . . . . . . . . . . . . . . . . . . . 157 25.3 Energy minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 26 Alternative sampling strategies 163 26.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 26.2 Alternative sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 27 Use of localized orbitals and bases in CASINO 165 27.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 27.2 Using CASINO to carry out ‘linear-scaling’ QMC calculations . . . . . . . . . . . . . . 167 28 Twist averaging in QMC 169 28.1 Periodic and twisted boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . 169 28.2 Using twisted boundary conditions in CASINO . . . . . . . . . . . . . . . . . . . . . . 170 28.3 Monte Carlo twist averaging within CASINO . . . . . . . . . . . . . . . . . . . . . . . 170 29 Finite-size correction to the kinetic energy 173 29.1 Finite-size correction due to long-ranged correlations . . . . . . . . . . . . . . . . . . . 173 4
29.2 Fourier transformation of CASINO’s two-body Jastrow factor . . . . . . . . . . . . . . 175 29.3 Fitting form for the long-ranged two-body Jastrow factor (3D) . . . . . . . . . . . . . 176 29.4 Fitting form for the long-ranged two-body Jastrow factor (2D) . . . . . . . . . . . . . 177 29.5 Applying the correction scheme in practice . . . . . . . . . . . . . . . . . . . . . . . . 177 30 Finite-size correction to the interaction energy 178 31 Electron–hole systems 178 32 Relativistic corrections to energies 179 33 Expectation values computable by CASINO 180 33.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 33.2 Density and spin density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 33.3 Reciprocal-space and spherical real-space pair-correlation functions . . . . . . . . . . . 188 33.4 Structure factor and spherically averaged structure factor . . . . . . . . . . . . . . . . 191 33.5 One-body density matrix, two-body density matrix and condensate fraction . . . . . . 193 33.6 Momentum density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 33.7 Localization tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 33.8 Dipole moment (molecules only) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 34 Atomic forces 197 34.1 Forces in the VMC method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 34.2 Forces in the DMC method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 34.3 The mixed DMC forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 34.4 The pure DMC forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 34.5 Implementation of forces in CASINO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 34.6 Explanation of the force estimators printed by CASINO . . . . . . . . . . . . . . . . . 201 35 The future-walking method 201 35.1 Derivation of the FW method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 35.2 The FW algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 35.3 Some practical advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 36 Noncollinear-spin systems 204 36.1 Wave functions for noncollinear-spin systems . . . . . . . . . . . . . . . . . . . . . . . 204 36.2 Spiral spin-density waves in the HEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 37 Magnetic fields and the fixed-phase approximation 205 37.1 Hamiltonian when an external magnetic field is present . . . . . . . . . . . . . . . . . 205 37.2 VMC in the presence of an external magnetic field . . . . . . . . . . . . . . . . . . . . 205 37.3 DMC in the presence of an external magnetic field . . . . . . . . . . . . . . . . . . . . 205 37.4 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 37.5 Applying magnetic fields in CASINO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 38 Analysis of the performance of CASINO on parallel computers 207 38.1 VMC in parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 38.2 Optimization in parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 5
Page 1 and 2: CASINO User’s Guide Version 2.13
Page 3: 8.6 GAUSSIAN94/98/03/09 . . . . . .
Page 7 and 8: 1 Introduction casino is a computer
Page 9 and 10: 3.2 Legal stuff casino is given awa
Page 11 and 12: - Grossman-Mitas DMC-DFT molecular
Page 13 and 14: Your defined setup can then be perm
Page 15 and 16: - : perform compilation (default).
Page 17 and 18: 6 Introductory user’s guide: how
Page 19 and 20: ATOM BASIS TYPE The basis used to r
Page 21 and 22: ENVMC v0.60: Script to extract VMC
Page 23 and 24: Std. err. in the mean DMC energy (a
Page 25 and 26: Jastrow factor from each cycle of t
Page 27 and 28: V(x) Ψ init (x) τ{ t Ψ 0 (x) x T
Page 29 and 30: the energy becomes roughly constant
Page 31 and 32: many cores, time limits etc, which
Page 33 and 34: Set the verbosity level of the mach
Page 35 and 36: 6.7 How to run coupled DFT-DMC mole
Page 37 and 38: unqmcmd --startqmc=M Start the chai
Page 39 and 40: config.out This is the name under w
Page 41 and 42: ‘slater-type’: use Slater-type
Page 43 and 44: CUSTOM SPAIR DEP (Block) This input
Page 45 and 46: initial configurations come from DM
Page 47 and 48: DTDMC (Real) Time step for DMC run
Page 49 and 50: FORCES INFO (Integer) Controls the
Page 51 and 52: nucleus is assumed to lie at the or
Page 53 and 54: MOVIECELLS (Logical) If F then casi
Page 55 and 56:
OPT MAXITER (Integer) Largest permi
Page 57 and 58:
of G vectors and discards all those
Page 59 and 60:
half a million cores, it may be des
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VM REWEIGHT (Logical) If vm reweigh
Page 63 and 64:
default this is 0 hartree. It shoul
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A very detailed specification of th
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-1 0 0 1 1 1 1 1 1 1 0 2 1 0 1 2 Pa
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cusp conditions; otherwise, only th
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Detailed information about each of
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|k| (outermost). Hence one can spec
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large and the wave function is near
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R(i) in atomic units 0.000000000000
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2. The charge-density Fourier coeff
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c_767: [ 996 ] ... Compressed expan
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valence charges for each atom %%%%%
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1988). This can be found online. An
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1.3813695578425E+00 1.3957621401173
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PWSCF Method: DFT DFT Functional: u
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0.125203784849961E-01 0.13042462855
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3.3000000000000E+00 2.0000000000000
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Potential Number of grid points 200
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9. Clearly, the total number of pos
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EBEST (DMC only) Best estimate of t
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Use G-vector set 1 Number of sets 2
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1000.0 rho_a(G)*rho_b(-G) 16.0 4.12
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total weight must always be include
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The exporter does not currently wor
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8.4.2 Generating gwfn.data files wi
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After successfully running properti
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% mv Test.FChk dna.Fchk run gaussia
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• By default, gaussian uses spin
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Routine Purpose qmc write Writes th
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not the case the defaults can be ch
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8.10 TURBOMOLE Website: www.turbomo
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• crysgen06/09, crystaltoqmc: The
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• quickblock: Simple reblocking u
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• In Movie Settings choose Trajec
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the move rejection probability is h
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This leads to the single-electron d
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In the UNR [19] scheme the modified
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13.7 Evaluating expectation values
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Population-control catastrophes sho
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where u k has the periodicity of th
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Although the constraint equations a
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18 Wave-function updating Consider
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19.2 Evaluating the nonlocal pseudo
Page 147 and 148:
of a unit point charge at r j in ev
Page 149 and 150:
19.4.3 1D Coulomb interaction Coulo
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To investigate whether the extrapol
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correlations, such as might be enco
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where n is the order of the expansi
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terms by definition, and it can be
Page 159 and 160:
which is therefore independent of r
Page 161 and 162:
where the local energy, E L , is E
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Another variant of variance minimiz
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The energy minimization method used
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valid. The first problem, which ari
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• Is emin min energy too high? Th
Page 171 and 172:
It may be activated by setting vmc
Page 173 and 174:
that the number of configuration mo
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• It is possible to use blip orbi
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0.5 0.5 0.0 particle 1 det 1 : 9 or
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The clearup twistav script can be u
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In the infinite system limit, the s
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Note that this has the k −2 diver
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• The effective time step, Eq. (3
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1 2 H He 1.00794 4.00260 3 4 5 6 7
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and the Dirac delta function is δ(
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33.2.2 Atomic densities K eywords:
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The spin-density matrix is a two-by
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33.3.3 Homogeneous and isotropic sy
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33.4 Structure factor and spherical
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33.5 One-body density matrix, two-b
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[ where the approximation ρ (1)T
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The figure shows the localization l
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with F HFT mix = − F P mix = −
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The input keyword to activate the c
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To each walker r j , we assign a li
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37 Magnetic fields and the fixed-ph
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38 Analysis of the performance of C
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the orbitals, α = 2 [11]. The use
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39.2 Implementation basics and perf
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• Use ‘endif’ and ‘enddo’
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• Evidence of testing on serial a
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B Appendix 2: Automatic testing of
Page 225 and 226:
• Delete any eepot.data and densi
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* "Generic" CASINO_ARCHs are intend
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- ‘head -n 1 /etc/redhat-release
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for a single job in an ensemble of
Page 233 and 234:
inary executable. CASINO does not r
Page 235 and 236:
otherwise. The following tags are o
Page 237 and 238:
[2] V.R. Saunders, R. Dovesi, C. Ro
Page 239 and 240:
[50] W. Janke, Statistical Analysis
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CASINO manual - Theory of Condensed Matter

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